Defence spokesman Chris Olukolade told reporters in Abuja that a heavily bearded Islamist fighter identified as Mohammed Bashir died during fighting in the town of Konduga, in Borno state.
Bashir, who was said to have had several aliases, had "been acting or posing on videos as the deceased Abubakar Shekau, the eccentric character known as leader of the group", he added.
The announcement marks the first time that Nigeria's military has said publicly that Shekau was dead after two previous claims by other security sources that he had died in 2009 and 2013.
Earlier this year, the spokeswoman for the country's secret police, Marilyn Ogar, said "the original Shekau is dead" and that the person appearing in videos was an imposter.
Olukolade said on Wednesday that the name "Shekau" had become a "brand name for the terrorists".
"The Nigerian military remains resolute to serve justice to anyone who assumes that designation or title as well as all the terrorists that seek to violate the freedom and territory of Nigeria."
Nigeria's military has been under pressure to regain territory lost to Boko Haram Islamists in the far northeast in recent weeks and said it has been conducting "coordinated air and land operations" to push back the militant fighters.
Olukolade claimed that during fighting in and around Konduga, a number of Boko Haram fighters were captured along with their equipment, while scores of others allegedly surrendered elsewhere.
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